1. **Stating the problem:** Solve the system of linear equations: First system: $$y = 2x + 1$$ $$y = -x + 7$$ 2. **Formula and rules:** To solve a system of equations, we find the values of $x$ and $y$ that satisfy both equations simultaneously. Since both expressions equal $y$, we can set them equal to each other. 3. **Set the equations equal:** $$2x + 1 = -x + 7$$ 4. **Solve for $x$:** $$2x + 1 = -x + 7$$ $$2x + x = 7 - 1$$ $$3x = 6$$ $$x = \frac{6}{3}$$ $$x = 2$$ 5. **Substitute $x=2$ back into one of the original equations to find $y$:** Using $$y = 2x + 1$$: $$y = 2(2) + 1$$ $$y = 4 + 1$$ $$y = 5$$ 6. **Solution:** The solution to the system is: $$(x, y) = (2, 5)$$ This means the two lines intersect at the point $(2, 5)$. The second system was not solved as per instructions to solve only the first system.